Inverse problems in cosmology and black hole spacetimes

Emory University, Atlanta GA

Investigators

Abstract

The interpretation of observed astrophysical data lies at the heart of modern cosmology and general relativity. Advancements in technology, including sensitive telescopes, high-energy neutrino detectors, and gravitational wave detectors, have revolutionized our ability to observe the universe. Modern astrophysics relies on mathematical properties of the initial conditions for the evolution of Einstein’s equations combined with numerical simulations used to analyze data and improve our understanding of the astrophysical systems. The objective of this research is to study inverse problems in astrophysics, which seek the underlying causes of observed astrophysical phenomena. This involves addressing mathematical questions such as uniqueness and stability for predictive models and developing efficient numerical reconstruction techniques. This research additionally has applications in fields such as medical imaging, while also offering opportunities for graduate student training and interdisciplinary collaborations. This proposal aims to investigate two challenges in cosmology and general relativity. The first project focuses on the recovery of the initial status of the universe from the Cosmic Microwave Background. The project will explore an X-ray tomography approach integrated with the physical model, especially the Einstein’s equations governing the evolution of the universe. Collaborative efforts will concentrate on advancing statistical inference techniques and developing numerical reconstruction algorithms. In addition, the project will study the mathematical properties of geodesic ray transforms in Lorentzian and pseudo-Riemannian geometry and address related rigidity questions. The second project seeks to extract information of black hole spacetimes using gravitational wave signals. The project will study the mathematical properties of black hole quasinormal modes and their relationship to black hole parameters. Furthermore, the project will study the scattering and inverse scattering problems for black hole spacetimes. The new investigations on the high energy stability and distribution of phase shifts will aim to offer insights that could be helpful for interpreting future scattering experiments. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.